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Physical Review A

Finite fourth-order squeezing of both quadrature phase components

Robert Lynch

Published Nov 1, 1987• 4 citations
Publisher

Abstract

In a previous Comment on recent papers by Hong and Mandel, I was able to show that the ``Jackiw state,'' which is infinitesimally different from the coherent state, displays fourth-order squeezing (as defined by Hong and Mandel's criterion) of both quadrature field components; the magnitude of such squeezing is, however, infinitesimal. In this paper an explicit perturbation calculation is given which results in a state with finite fourth-order squeezing of both quadrature components.

DOI
10.1103/physreva.36.4501

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sComment on 'Puri's criterion and higher-order squeezing'

Xia Yunjie, Yan Ke-zhu, Kong Xianghe

The result that Lynch and Mavromatis [Phys. Rev. A 52, 55 (1995)] obtained by Puri's definition of squeezing has no relation to Hong and Mandel"s higher-order squeezing [Phys. Rev. Lett. 54, 323 (1985)]. We also point out that, for an electromagnetic field, the nonclassicality of the squeezed state defined according to Puri's general uncertainty relation is not preserved.

Physical Review A•Feb 1, 1997•4 citations
In a previous Comment on recent papers by Hong and Mandel, I was able to show that the ``Jackiw state,'' which is infinitesimally different from the coherent state, displays fourth-order squeezing (as defined by Hong and Mandel's criterion) of both quadrature field components; the magnitude of such squeezing is, however, infinitesimal. In this paper an explicit perturbation calculation is given which results in a state with finite fourth-order squeezing of both quadrature components.
Hong and Mandel have recently suggested a scheme which allows generalization of ``squeezing'' to higher-order (even) moments of the electromagnetic field. The new criterion for squeezing is that the expectation value of the moment be less than that for the coherent state. In this paper it is explicitly shown that both electric-field quadrature components are squeezed to fourth order in a ``Jackiw state,'' thus proving that the coherent state does not minimize the fourth-order uncertainty product. The implications of this result for Hong and Mandel's proposal are briefly considered.
It is shown that a particular combination of so-called even coherent state dubbed the orthogonal-even coherent state, while exhibiting no ``ordinary'' or second-order squeezing, can furnish near-optimal simultaneous-quadrature fourth-order squeezing [where the latter term is defined in the sense of Hong and Mandel, Phys. Rev. Lett. 54, 323 (1985)]. The Wigner function of the particular quantum-mechanical superposition of states is calculated and various plots compared to the Wigner function of a simple statistical mixture of the same states. Rather uninteresting behavior is found in the latter case, which illustrates that the higher-order squeezing effect is due to nonclassical, quantum-mechanical ``interference in phase space.''
Recently, Puri revisited the usual uncertainty relation arguments. Utilizing a well-known and sharpened version of the uncertainty relation, he has proposed an alternative squeezing criterion for the case of noncanonical operators. We investigated this in the hope that Puri's proposal might allow one to define a higher-order squeezing criterion that would avoid an anomaly found with the standard Hong-Mandel (HM) scheme, i.e., the possibility of simultaneous-quadrature squeezing. However, it is found that higher-order squeezing based on Puri's squeezing criterion has what one might judge to be an even worse and unphysical defect than the HM scheme, in that even at the squeezing ``trigger level,'' squeezing in one quadrature is necessarily accompanied by considerable antisqueezing in the other quadrature.